Joint Symposium, 7 – 18 February 2022
Week 1 (7 – 11 Feb): Online via Zoom
Week 2 (14 – 18 Feb): On-site at MATRIX, Creswick
The research symposium explored Nijenhuis geometry and uses it as a link connecting finite and infinite dimensional integrable systems. We use the methods and results of infinite dimensional integrable systems to attack famous conjectures in the theory of finite-dimensional integrable systems, in particular concerning existence, description and classification of polynomially integrable geodesic flows on the torus and on the sphere.
We employ recent advances in projective geometry and the theory of separation of variables to construct and study new examples of multicomponent integrable systems.
While Riemannian and Poisson geometries have been very well studied, Nijenhuis geometry is a relatively new research area. In the first online week of the workshop, an introduction to Nijenhuis geometry was given. We presented a general research programme in the area and will show that it is realistic by presenting first nontrivial easy-to-formulate results. We discussed milestones of the theory, open problems, and sketch possible applications.
Alexey Bolsinov works as a Reader in Mathematics at Loughborough University. His research results include the discovery of a new phenomenon in dynamical systems known as integrable chaos, theory of orbital classification for integrable two-degrees-of-freedom systems, loop molecule method in topology of integrable systems and new classes of holonomy groups and symmetric spaces in pseudo-Riemannian geometry. Under his supervision, 18 PhD students successfully completed their research projects, many of them continue their academic careers in USA, Russia, Brazil, Germany and China.
Vladimir Matveev is a Chair of Mathematics at the University of Jena. He has solved a number of major open problems in several areas of Difierential Geometry and in the theory of Integrable Systems including two problems explicitly posed by Sophus Lie in 1882, the projective Lichnerowich conjecture and c-projective Yano-Obata conjecture. He constructed two new examples of natural integrable Hamiltonian systems on closed surfaces, Dullin-Matveev and Matveev-Shevchishin systems.
Symposium companion seminars: Playlist includes pre-recorded lectures by Alexey Bolsinov and Andrey Konyaev. These lectures were recorded as part of a cooperation between the Chinese-Russian Mathematical Center (Beijing) and the Moscow Center of Fundamental and Applied Mathematics (Moscow). Watch Sino-Russian Center seminars on YouTube
Companion seminars lecture slides (PDFs): Lecture1_Nijenhuis, Lecture2_Nijenhuis, Lecture3_Nijenhuis, Lecture4_Nijenhuis, Lecture5_Nijenhuis, Lecture6_Nijenhuis, Lecture7_Nijenhuis, Lecture8_Nijenhuis, Lecture9_Nijenhuis, Lecture10_Nijenhuis, Lecture11_Nijenhuis, Lecture12_Nijenhuis, Lecture13_Nijenhuis, Lecture14_Nijenhuis, Lecture15_Nijenhuis, Lecture_16, Lecture_17, Lecture_18, Lecture_19, Lecture20_Nijenhuis, Lecture21_Nijenhuis, Lecture22_Nijenhuis
Nijenhuis Geometry and Integrable Systems seminars: Playlist includes pre-recorded lectures on Nijenhuis Geometry for ECRS, Chair’s Talks, as well as Zoom and Local Talks. Watch Nijenhuis Geometry Symposium seminars on YouTube
For more information, please visit the MATRIX symposium webpage.